package Text4;

import java.util.*;

public class Main {
    //    //如果 N = p1^c1 * p2^c2 * ... *pk^ck
//    //约数个数： (c1 + 1) * (c2 + 1) * ... * (ck + 1)
    static int mod = (int) 1e9 + 7;

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Map<Integer, Integer> map = new HashMap<>();
        int m = in.nextInt();
        while (m-- > 0) {
            int n = in.nextInt();
            for (int i = 2; i <= n / i; i++) {
                if (n % i == 0) {
                    int s = 0;
                    while (n % i == 0) {
                        n /= i;
                        s++;
                    }
                    map.put(i, map.getOrDefault(i, 0) + s);
                }
            }
            if (n > 1) {
                map.put(n, map.getOrDefault(n, 0) + 1);
            }
        }
        long res = 1;
        for (int val : map.values()) {
            res = res * (val + 1) % mod;
        }
        System.out.println(res);
    }
}
